### All GMAT Math Resources

## Example Questions

### Example Question #11 : Understanding Functions

Define the operation as follows:

Solve for :

**Possible Answers:**

**Correct answer:**

### Example Question #11 : Understanding Functions

Define , where .

Evaluate in terms of and .

**Possible Answers:**

**Correct answer:**

This is equivalent to asking for the value of for which , so we solve for in the following equation:

Therefore, .

### Example Question #12 : Understanding Functions

Define an operation as follows:

For any real numbers ,

Evaluate .

**Possible Answers:**

**Correct answer:**

### Example Question #13 : Understanding Functions

An infinite sequence begins as follows:

Assuming this pattern continues infinitely, what is the sum of the 1000th, 1001st and 1002nd terms?

**Possible Answers:**

**Correct answer:**

This can be seen as a sequence in which the term is equal to if is not divisible by 3, and otherwise. Since 1,000 and 1,001 are not multiples of 3, but 1,002 is, the 1000th, 1001st, and 1002nd terms are, respectively,

and their sum is

### Example Question #14 : Understanding Functions

Define . What is ?

**Possible Answers:**

**Correct answer:**

This can best be solved by rewriting as and using the power of a power property.

### Example Question #15 : Understanding Functions

is defined as the least integer greater than or equal to .

is defined as the greatest integer less than or equal to .

Define .

Evaluate .

**Possible Answers:**

**Correct answer:**

### Example Question #16 : Understanding Functions

Define an operation as follows:

For any real numbers ,

.

Evaluate .

**Possible Answers:**

**Correct answer:**

### Example Question #11 : Functions/Series

is defined as the least integer greater than or equal to .

Define .

Define .

Evaluate .

**Possible Answers:**

**Correct answer:**

First, evaluate :

Now, evaluate :

### Example Question #17 : Understanding Functions

is defined as the greatest integer less than or equal to .

Solve for :

**Possible Answers:**

**Correct answer:**

means that the greatest integer less than or equal to is 7. The equivalent statement is

.

Solve for as follows:

or, in interval form,

### Example Question #18 : Understanding Functions

Which of the following pairs of statements is sufficient to prove that does not have an inverse?

**Possible Answers:**

None of these pairs of statements would be sufficient to prove that does not have an inverse.

is not defined for , is not defined for ,

**Correct answer:**

For a function to have an inverse, no -coordinate can be paired with more than one -coordinate. Of our choices, only

causes this to happen.

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